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NEET
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Physics
Chapter
Center of Mass, Momentum and Collision

NEET · Physics · Center of Mass, Momentum and Collision

The position-time (x-t) graph of a moving body of mass 2 ~kg is...

The position-time (x−t)(x-t) graph of a moving body of mass 2 kg2 \mathrm{~kg} is shown in the figure. The impulse on the body at t=4 st=4 \mathrm{~s} is The position-time (x-t) graph of a moving body of mass 2 ~kg is shown in the figure. The impulse on the body at t=4 ~s

Options

  1. A1.5 kg−ms−11.5 \mathrm{~kg}-\mathrm{ms}^{-1}
  2. B−1.5 kg−ms−1-1.5 \mathrm{~kg}-\mathrm{ms}^{-1}
  3. C1 kg−ms−11 \mathrm{~kg}-\mathrm{ms}^{-1}
  4. D2 kg−ms−12 \mathrm{~kg}-\mathrm{ms}^{-1}

Correct answer

B. −1.5 kg−ms−1-1.5 \mathrm{~kg}-\mathrm{ms}^{-1}

Step-by-step solution

Here, mass of the body, m=2 kgm=2 \mathrm{~kg} and time, t=4  s\mathrm{~s}Impulse =pf−pi=p_f-p_i where, pi=p_i= initial momentum, pf=p_f= final momentum Impulse =mvf−mvi=m(vf−vi)(∵p=mv)\quad=m v_f-m v_i=m\left(v_f-v_i\right) \quad(\because p=m v) As from the graph, v_f=3−38−4=\frac{3-3}{8-4}=0  and \text{ and }v_i=3−04−0=34 Impulse =\frac{3-0}{4-0}=\frac{3}{4} \text{ Impulse }=2 \times\left(0-\frac{3}{4}\right)=-1.5 \mathrm{~kg}-\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm{ms}^{-1}Hence, the correct option is (b).
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